Mathematical analysis and modeling of the evolution of magnetoelastic materials

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Magnetoelastic materials have been of technological and academic interest for decades due to their fascinating properties and various applications, e.g., as actuators and sensors in aeronautics, biomedicine, energy technology etc. Several novel materials have been found and studied like giant magnetostrictive materials, magnetoelastic membranes, ferromagnetic shape-memory alloys, magnetoelastic metamaterials and foams or magnetic fluids. A thorough mathematical understanding of such materials requires advanced analytical tools and interdisciplinary cooperations with engineers and physicists. In this project we focus on innovative time-dependent mathematical models for magnetoviscoelastic materials allowing for large deformations and micromagnetism. While there is quite some literature on static models for magnetoelastic materials, the publications on time-dependent systems are largely limited to either elastic or magnetic effects. For the coupling of elastic effects, magnetic effects and temporal evolution, we apply a novel approach which was initiated and developed by the PI, former members of her team and Chun Liu. For homogeneous materials, several results on the existence and uniqueness of solutions have been proved yet, also as part of the ongoing project. The objective of this proposal is to advance the modelling of heterogeneous magnetoviscoelastic materials with the help of sharp as well as diffuse interface models. At interfaces of heterogeneous materials, mechanical and/or magnetic properties change drastically. This yields a weaker regularity that causes special mathematical challenges in the analytical investigation of the well-posedness of the corresponding systems of partial differential equations. In addition, we will intensify the interdisciplinary discussion on the mathematical modeling of magnetoviscoelastic materials required for a well-founded understanding of such materials and will thus also promote the transfer of knowledge from mathematical research to materials science.